Despite the might of the United States, President Bush is not necessarily always the top dog.
In the immediate aftermath of the 9/11 attacks in America, Mr Blair looked more decisive and strong than the beleaguered President. But in the run-up to the Iraq war, President Bush was calling the shots and the Prime Minister was struggling to keep hold of the leash.
When the two leaders met in the margins of this week's United Nations summit in New York, there was no doubt who was up and who down. Hurricane Katrina has battered the President too. In contrast, the political climate in Britain is better for Mr Blair than he could have imagined when he won his third term.
Unusually, the two buddies did not appear before the cameras after their chat. Evidently, they did not want to face difficult questions about the daily carnage in Iraq.
They discussed when to scale down their military presence in Iraq, as they both wish to do. They instinctively agreed that the troops could not possibly be pulled out while acts of insurgency continue, because it would look like rewarding the terrorists, and to wait until the Iraqis can handle security by themselves.
The Iraqi army is judged well short of being able to do that and the police force even further behind. So there was no option for the two leaders but to repeat the well-worn mantra that they will "stay the course and finish the job", even if that does not suit their domestic timetable - notably America's mid-term elections next year.
As if the problems in Iraq were not bad enough, the Prime Minister and President acknowledged that another crisis is looming next door in Iran over its apparent determination to press ahead with a nuclear weapons programme.
As Mr Blair returned to London yesterday, the words of Mahmoud Ahmadinejad, Iran's new President, were ringing in his ears. Ominously, he offered to share Iran's nuclear secrets with other Muslim countries.
Mr Blair fears that Iran is going to be a huge issue over the next few months.
President Bush and Mr Blair have something else in common. They are both serving their final term and might even leave office in the same year - 2008. That they have no need to seek re-election does not insulate them from the normal pressures of political life.
The label "lame duck" is starting to stick to Mr Bush. Mr Blair's time will doubtless come. At this week's TUC conference, trade union leaders, desperate for their brief annual fix of publicity, began rehearsing their argument to the Prime Minister: "As you are going to go, you might as well get on with it."
For now, Mr Blair is still firing on all cylinders. Indeed, he seems restless to sort out the whole world's problems before he bows out. The G8 summit at Gleneagles increased aid and debt relief for Africa. Battle will soon resume in his attempt to persuade the European Union to embrace economic reform and dismantle its Common Agricultural Policy.
In New York, Mr Blair added another one to his list: he vowed to try to break the looming deadlock over vital World Trade Organisation talks in Hong Kong in December.
For all the progress on helping Africa, the continent needs America and Europe to dismantle the agricultural subsidies that prevent African producers competing on a level playing field.
Yet all this activity has a downside. Some Blair advisers worry he is not devoting enough time to the domestic front. After his summer holiday in the Caribbean, he squeezed in a speech on antisocial behaviour before leaving for a trip to China and India. Then, after a speech on education, he departed for New York.
Tomorrow's election in Germany will put the spotlight back on to Europe's ability to reform. But Mr Blair will try to devote most of the coming week to domestic matters in the run-up to the Labour conference starting a week tomorrow, where he wants to showcase policies on education, health and bringing back "respect". However, he also needs to address terrorism after the London bombings, and that will inevitably raise the question of whether the Iraq war increased the threat to Britain. All roads lead back to Iraq.
Mr Blair does not want his legacy to be the Iraq war or foreign affairs generally. He would much prefer to focus on "education, education, education" but, with Britain holding the presidency of the G8 and EU, events have ensured that this year will be dominated by international affairs.
As he made clear on BBC Radio 4 yesterday, his priority is to make "irreversible" his public-sector reforms so that they cannot be undone by any future government. But time is running out for him. "We have put a load of money in, but the results have been patchy," one Blarite minister admitted. "What people want now is not more money but better services." In many ways, the cash was the easy bit. Making services more consumer-orientated is much harder.
For the rest of this year, Mr Blair will try to tilt the balance back towards the domestic front. It will not be easy. One close ally told me: "The danger is that he will be remembered as a foreign policy Prime Minister."Reuse content